There are number of possibilities here:
1- Giving users the ability to edit posts and add notes. This is not something you want to do. As it might create many issues for you. However, you can use a Wiki plugin if you want to pursue this option.
2- Enabling notes through comments. This is a better option. You can handle user comments and ask whether he wants to add it as a comment or a note to be added to the post. You need to modify WordPress code and develop your own code as well.
3- Using footnotes plugin as notes system. You can use any of the plugins available for footnotes and possibly customize it yo use it a notes system. This plugin seems to be good. It displays the footnote inside the text. You can modify the plugin code to display a note instead of a footnote.
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